Localization and quasilocalization of a spin-$1/2$ fermion field on a two-field thick braneworld

Localization of a spin-1/2 fermion on the braneworld is an important and interesting problem. It is well known that a five-dimensional free massless fermion. minimally coupled to gravity cannot be localized on the Randall-Sundrum braneworld. In order to trap such a fermion, the coupling between the fermion and bulk scalar fields should be introduced. In this paper, localization and quasilocalization of a bulk fermion on the thick braneworld generated by two scalar fields (a kink scalar phi and a dilaton scalar pi) are investigated. Two types of couplings between the fermion and two scalars are considered. One coupling is the usual Yukawa coupling -eta(Psi) over bar phi Psi between the fermion and kink scalar, another one is lambda(Psi) over bar Gamma(M)partial derivative(M)pi gamma 5 Psi . between the fermion and dilaton scalar. The left-chiral fermion zero mode can be localized on the brane, and both the left-and right-chiral fermion massive Kaluza-Klein modes may be localized or quasilocalized. Hence the four-dimensional massless left-chiral fermion and massive Dirac fermions, whose lifetime is infinite or finite, can be obtained on the brane.